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Find the volume of the right circular cone with
(i) radius 6 cm, height 7 cm
(ii) radius 3.5 cm, height 12 cm
(i) Radius (r) of cone = 6 cm
Height (h) of cone = 7 cm
Volume of cone
Therefore, the volume of the cone is 264 cm3.
(ii) Radius (r) of cone = 3.5 cm
Height (h) of cone = 12 cm
Volume of cone
Therefore, the volume of the cone is 154 cm3.
The height of a cone is 15 cm. If its volume is 1570 cm 3 , find the radius of the base.
(Use π = 3.14)
given
h = 15 cm
volume of cone = 1570
to find- radius (r)
formula-
volume of cone =
1570 = 3.14 * * 15 /3
1570 *3 = 3.14 * 15 *
= 1570 * 3 / 3.14 * 15
=100
taking square roots on both sides , we get
r = 10 cm
The volume of a right circular cone is 9856 cm3 . If the diameter of the base is 28 cm,
find
(i) height of the cone
(ii) slant height of the cone
(iii) curved surface area of the cone
(i) Radius of cone = 
Let the height of the cone be h.
Volume of cone = 9856 cm3
h = 48 cm
Therefore, the height of the cone is 48 cm.
(ii) Slant height (l) of cone 
Therefore, the slant height of the cone is 50 cm.
(iii) CSA of cone = πrl
= 2200 cm2
Therefore, the curved surface area of the cone is 2200 cm2.
Find the capacity in litres of a conical vessel with
(i) radius 7 cm, slant height 25 cm
(ii) height 12 cm, slant height 13 cm
(1)- Given,
radius of a cone, r =7cm,and
Slant height, l =25cm
Let the height of the cone be =h cm
Since,we know that
Height (h) of cone 
Now,
Capacity of a vessel=volume of cone
Volume of cone
Therefore, capacity of the conical vessel
= 
= 1.232 litres
(2)Given,
Height,h= 12cm,and
Slant height, l =13cm
Let,radius of cone = r cm
Since we know that
Radius (r) of cone 
Volume of cone
Therefore, capacity of the conical vessel
= 
= 
litres
A conical pit of top diameter 3.5 m is 12 m deep. What is its capacity in kilolitres?
Diameter of the conical pit = 3.5m
radius= 1.75m
height=12m
volume of cone= π h /3
= 3.14 * 1.75^2 * 12 /3
=115.39/3
= 38.46
volume of cone = 38.46 m^3
1= 1000 L = 1 kilolitre
hence ,
38.5 = 38.5 kilolitrs
A right triangle ABC with sides 5 cm, 12 cm and 13 cm is revolved about the side 12 cm.
Find the volume of the solid so obtained.
A right triangle ABC with sides 5 cm, 12 cm and 13 cm is revolved about the side 12 cm - this suggests that the solid so formed is a right circular cone with slant height (l) = 13 cm, height (h) = 12 cm and radius of base (r) = 5 cm.
Volume of cone 
∴ Volume of the right circular cone = 314 cm³
If the volume of a right circular cone of height 9 cm is 48? cm3, find the diameter of its base.
Volume of a right circular cone =
(Equation 1)
Here, h = 9cm and Volume of the right circular cone = 48π cm³
So, equation 1 becomes;
Diameter of its base = 2r = 8cm
A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m.
Find its volume. The heap is to be covered by canvas to protect it from rain. Find the area of the canvas required.
Diameter of the cone = 10.5m (Radius of the cone = 5.25m)
Height of the cone = 3m
Volume of the cone = (πr²h)/3
∴ Volume of the cone = (π x 5.25² x 3)/3 = 86.625m³
The heap is to be covered by canvas to protect it from rain and we have to find the area of the canvas required. So, that means, we have to find the lateral surface area.
Lateral surface area of the cone = πr√r² + h²
∴ Lateral surface area of the cone = π x 5.25√5.25² + 3² = 99.77m²
∴ The area of the canvas required = 99.77m²
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